Today, three-dimensional imaging is a widely established technique in the field of medical diagnosis. A series of established techniques like magnetic resonance imaging (MRI), computed tomography (CT), optical coherence tomography (OCT), positron emission tomography (PET), single-photon emission computed tomography (SPECT) and ultrasonic imaging (US), as well as various specialized or experimental and less common techniques allow the acquisition of three-dimensional scans. Such volumetric scans are usually built by collecting a series of subsequent two-dimensional scans (slices) at slightly shifted positions (targeting a uniform intra-slice distance) and reconstructing a 3D scan from these single slices. The corresponding image data usually comprises image values (such as luminance and/or color values etc.) for a three-dimensional grid of voxels. “Voxel” designates a volume element of the grid, represented by one or a plurality of the image values mentioned.
Compared to two-dimensional medical imaging, the third spatial dimension delivers a significant information gain and often leads to more insight supporting the diagnosis.
A major drawback in medical imaging arises from image noise which occurs in almost every acquisition method and leads to an irregular granular pattern. In MRI, noise is influenced by the resistance of the receiving coil and by inductive losses in the sample and depends on the static magnetic field and the sample volume size. Noise in magnitude MRI images is Rician distributed, based on the assumption of zero-mean uncorrelated Gaussian noise in the real and the imaginary signal parts. CT shows the Poisson distributed X-ray noise characteristics and depends on the number of photons that leave the source, the amount of photons that pass unaffected through the sample, those who are captured by the detector, and those which underlie scattering and also surrounding light photons. OCT suffers from speckle noise its origin lying in the coherent nature of this scanning technique. Multiple scattering in the tissue manipulates the incoming light waves in the sense of a two-dimensional random walk (real and imaginary dimension). This leads to identically normal distributed real and imaginary components with zero mean and identical standard deviation that causes the noise magnitude to follow a Rayleigh distribution.
Even though the cause and characteristic of the noise differs from modality to modality, its influence to the information content of the image is always degrading. While noise reduction for two-dimensional images is and has been prospected very actively since decades, three-dimensional denoising mainly came in focus with the emerging research in volumetric imaging and only limited efforts for specialized volume denoising methods has been made so far, often by adapting known 2D-filters to an additional dimension. Established and well known methods in this category are the Lee filter (J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images”, Graph. Model. Im. Proc. 17(1), 24-32, 1981), the Frost filter (V. S. Frost, J. A. Stiles, A. Josephine, K. S. Shanmugan, and J. C. Holtzman, “A model for radar images and its application to adaptive digital filtering of multiplicative noise”, IEEE Trans. Pattern Anal. Mach. Intell. 4(2), 157-166, 1982), the Anisotropic diffusion (P. Perona and J. Malik, “Scale-Space and Edge Detection Using Anisotropic Diffusion”, IEEE Trans. Pattern Anal. Mach. Intell., vol. 12, no. 7, pp. 629-639, 1990) and Total Variation minimization (L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms”, Physica D 60, 259-268, 1992), all extended to a three-dimensional neighborhood.
Due to the fact that 3D images normally feature a substantially more complex information structure than 2D images (e.g. edges in 2D are surfaces in 3D), such direct extensions may not be able to consider the 3D information efficiently. Adaptations and variations therefore try to improve the information consideration of the third dimension as much as possible. The Anisotropic Diffusion was adapted and combined for 3D volumetric data by several approaches in the past years. Other studies cover volumetric denoising by 3D wavelet transformation, Non-Local Means, sparseness and self-similarity, local surface approximation, and others. Some research has also been done in terms of 4D denoising (volumetric plus time).
But still, for many situations the major part of these adapted approaches often deliver insufficient results, especially for subsequent processing steps like image segmentation or content recognition in the context of strong noise occurrence.